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Unfortunately, you'll have to use a 3rd party app for this. This option was embedded in older Xperias but was removed for some reason. My advise is to use Google Messenger, it's a Google app so you can consider it a 1st party application somehow and it has this functionality.
https://play.google.com/store/apps/details?id=com.google.android.apps.messaging&hl=en
Hi,
Unfortunately, with the preinstalled messaging application there is no function to block messages from a sender. But I will forward your feedback internally.
What I can recommend instead is that you use Hangouts (it's preinstalled) for SMS. From this application you can block a sender. Go to Settings > More > Default SMS app > Hangouts. If you now open Hangouts, you will see that your other messages is displayed in Hangouts. If you see a contact/number that you would like to block, tap it so the conversation opens > Tap the menu button (three dots) > People & options > Block <number/name>.
These message will still reach your phone, but they will end up in the Archived conversations (via Hangouts) and you will not receive any notification for these messages.